Estimating the Recovery Rates for Unsecured Loans to Small Sized Firms
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Masahiro Toshiro
Abstract
We analyze the recovery rates of 66,928 Japanese unsecured loans in default by ordered logistic regression. We divide the defaulted firms by sole proprietorships and industrial corporations and analyze the recovery rates for each type of firms. The recovery rate for sole proprietorships is larger than that for industrial corporations. Moreover, we model not only the recovery rate during five years at the time of default but also that evaluated at the time of loan appraisal for each type of firms, and we call them “loan model” and “after-default model” respectively. The significant factors with large regression coefficients are different for each model and each type of firms. We find that these are (1) guarantee by business owner’s family in two models for each type of firms, (2) firm age in two models for industrial corporations, (3) exposure rate at default in the after-default model for each type of firms, (4) obligor’s real-estate value minus debt amount, initial loan amount, and white tax return in the loan model for sole proprietorships. The values of Somers’ D for the after-default model are larger than those for the loan model because the exposure rate at default which has large estimates can be available at time of default. The values of Somers’ D for sole proprietorships are larger than those for industrial corporations. We divide all defaulted loans into four classes based on the score evaluated by the model, and validate the ratings of the actual recovery rates through three kinds of statistical tests. In addition, we conduct out-of-sample tests, and examine the usefulness of the model.
Note
Any views or opinions expressed in this paper are solely those of the authors and do not necessarily represent those of Micro Business and Individual Unit of Japan Finance Corporation.
Appendix
A Variable list used for Step 3
Financial accounting variables and attribute variables are listed below as candidates for Step 3.
Financial accounting variable list.
| Financial accounting variables | S.P.(*1) | I.C.(*2) | abbreviated description | |
|---|---|---|---|---|
| F01 | Sales amount | x | x | Sales |
| F02 | Net sales amount | x | x | Net sales |
| F03 | Sales cost | x | x | Sales cost |
| F04 | Gross profit | x | x | Gross profit |
| F05 | Selling, general and administrative expenses | x | x | Selling expenses |
| F06 | Labor cost | x | x | Labor cost |
| F07 | Depreciation cost | x | x | Depreciation cost |
| F08 | Operating profit | x | x | Operating profit |
| F09 | Non-operating expenses | x | x | Non-operating expenses |
| F10 | Interest expenses | x | x | Interest expenses |
| F11 | Profit before income taxes | x | x | Profit before income taxes |
| F12 | Current assets | x | x | Current assets |
| F13 | Cash and deposits | x | x | Cash and deposits |
| F14 | Accounts receivable-trade | x | x | Accounts receivable |
| F15 | Inventories | x | x | Inventories |
| F16 | Other current assets | x | x | Other current assets |
| F17 | Non-current assets | x | x | Non-current assets |
| F18 | Assets | x | x | Assets |
| F19 | Current liabilities | x | x | Current liabilities |
| F20 | Accounts payable-trade | x | x | Accounts payable |
| F21 | Other current liabilities | x | x | Other current liabilities |
| F22 | Non-current liabilities | x | x | Non-current liabilities |
| F23 | Long-term debt | x | x | Long-term debt |
| F24 | Liabilities | x | x | Liabilities |
| F25 | Average monthly principal repayment for long-term debt | x | x | Monthly repayment |
| F26 | Labor costs for representatives and family members | x | x | Labor costs for M |
| F27 | Real-estate value minus debt amount (log value) | x | Real-estate minus debt | |
| F28 | Non-current assets minus non-current liabilities (log value) | x | Non-current A minus L |
*1 S.P.: Sole proprietorships, *2 I.C.: Industrial corporations
Attribute variable list.
| Model | Loan | After-default | ||||
|---|---|---|---|---|---|---|
| Attribute variables | S.P.(*1) | I.C.(*2) | S.P.(*1) | I.C.(*2) | abbreviated description | |
| A01 | Firm age (*3) | x | x | x | x | Firm age |
| A02 | Number of employers | x | x | x | x | Number of employers |
| A03 | Initial loan amount (log value) | x | x | x | x | Initial loan amount |
| A04 | Guarantee by business owner’s family dummy | x | x | x | x | Guarantee dummy |
| A05 | Manufacturing industry dummy | x | x | x | x | Manufacturing I.dummy |
| A06 | Construction industry dummy | x | x | x | x | Construction I.dummy |
| A07 | Wholesale and retail trade industry dummy | x | x | x | x | Wholesale I.dummy |
| A08 | Accommodations, eating and drinking services industry dummy | x | x | x | x | AED services I.dummy |
| A09 | Medical, healthcare and welfare industry dummy | x | x | x | x | Medical I.dummy |
| A10 | Service industry dummy | x | x | x | x | Service I.dummy |
| A11 | Real estate industry dummy | x | x | x | x | Real estate I.dummy |
| A12 | Transport industry dummy | x | x | x | x | Transport I.dummy |
| A13 | Loan of working capital dummy | x | x | x | x | Working capital dummy |
| A14 | Repayment period | x | x | x | x | Repayment period |
| A15 | White tax return dummy | x | x | x | x | White tax return dummy |
| A16 | Owner’s age(*3) | x | x | x | x | Owner’s age |
| A17 | EAD rate (EAD divided by initial loan amount) | x | x | EAD rate | ||
| A18 | EAD (log value) | x | x | EAD | ||
*1 S.P.: Sole proprietorships, *2 I.C.: Industrial corporations, *3 Firm age and owner’s age at providing loan are used in the loan model, whereas those at default are used in the after-default model.
B EAD-weighted actual RR
B.1 In-sample tests
Table 18 shows the EAD-weighted actual RRs for loans to sole proprietorships. The EAD-weighted actual RRs of each rating are also given in a proper order in both the loan model and after-default model as well as Table 6.
EAD-weighted actual RR for loans to sole proprietorships.
| Loan model | After-default model | ||||||
|---|---|---|---|---|---|---|---|
| Rating | N | EAD composition ratio | EAD-weighted actual RR | Rating | N | EAD composition ratio | EAD-weighted actual RR |
| A | 3,695 | 16 % | 39 % | A | 7,441 | 10 % | 56% |
| B | 3,694 | 26 % | 25 % | B | 7,445 | 22 % | 31 % |
| C | 3,694 | 20 % | 17 % | C | 7,450 | 30 % | 23 % |
| D | 3,695 | 38 % | 12 % | D | 7,436 | 38 % | 14 % |
| All | 14,778 | 100 % | 21 % | All | 29,772 | 100 % | 25 % |
The EAD-weighted actual RRs for loans to industrial corporations are shown in Table 19, and they are also in a proper order as well as sole proprietorships in Table 18.
EAD-weighted actual RR.
| Loan model | After-default model | ||||||
|---|---|---|---|---|---|---|---|
| Rating | N | EAD composition ratio | EAD-weighted actual RR | Rating | N | EAD composition ratio | EAD-weighted actual RR |
| A | 7,465 | 26 % | 15 % | A | 9,290 | 13 % | 25 % |
| B | 7,466 | 23 % | 13 % | B | 9,288 | 27 % | 14 % |
| C | 7,464 | 25 % | 10 % | C | 9,292 | 32 % | 9 % |
| D | 7,465 | 25 % | 7 % | D | 9,286 | 28 % | 7 % |
| All | 29,860 | 100 % | 11 % | All | 37,156 | 100 % | 12 % |
B.2 Out-of-sample tests
We show the EAD-weighted actual RRs for loans to sole proprietorships in the out-of-sample tests. Table 20 shows they are in a proper order as well as Table 12.
EAD-weighted actual RR for loans to sole proprietorships defaulted in FY2012.
| Loan model | After-default model | |||||
|---|---|---|---|---|---|---|
| N | (ratio) | Actual RR | N | (ratio) | Actual RR | |
| A | 1,017 | (22 %) | 41 % | 1,258 | (20 %) | 52 % |
| B | 1,041 | (23 %) | 25 % | 1,729 | (27 %) | 31 % |
| C | 1,149 | (25 %) | 17 % | 1,841 | (29 %) | 21 % |
| D | 1,357 | (30 %) | 12 % | 1,477 | (23 %) | 13 % |
| All | 4,564 | (100 %) | 20 % | 6,305 | (100 %) | 22 % |
Table 21 shows the EAD-weighted actual RRs for loans to industrial corporations defaulted in FY2012 are also in a proper order as well as sole proprietorships in Table 20.
EAD-weighted actual RR for loans to industrial corporations defaulted in FY2012.
| Loan model | After-default model | |||||
|---|---|---|---|---|---|---|
| N | (ratio) | Actual RR | N | (ratio) | Actual RR | |
| A | 1,759 | (24 %) | 17 % | 2,423 | (29 %) | 20 % |
| B | 1,716 | (24 %) | 13 % | 2,381 | (29 %) | 14 % |
| C | 1,919 | (27 %) | 11 % | 1,895 | (23 %) | 11 % |
| D | 1,839 | (25 %) | 7 % | 1,620 | (19 %) | 8 % |
| All | 7,233 | (100 %) | 12 % | 8,319 | (100 %) | 13 % |
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Articles in the same Issue
- Editorial
- Guest Editors’ Note on the Summer 2019 Special Issue – New Solutions in Risk Management
- Featured Articles
- Regularized Regression for Reserving and Mortality Models
- Estimating the Recovery Rates for Unsecured Loans to Small Sized Firms
- Factors Widening the Gap between Hypothetical and Actual choices—Empirical Evidence from the Japanese Medical Insurance Market—
- Ordinary and Markov-Switching Autoregressive Models for Firm-Level Underwriting Data
Articles in the same Issue
- Editorial
- Guest Editors’ Note on the Summer 2019 Special Issue – New Solutions in Risk Management
- Featured Articles
- Regularized Regression for Reserving and Mortality Models
- Estimating the Recovery Rates for Unsecured Loans to Small Sized Firms
- Factors Widening the Gap between Hypothetical and Actual choices—Empirical Evidence from the Japanese Medical Insurance Market—
- Ordinary and Markov-Switching Autoregressive Models for Firm-Level Underwriting Data
